Year: 2025
Type: article
Abstract: Colcombet and Petris ¸an argued that automata may be usefully considered from a functorial perspective, introducing a general notion of "V -automaton" based on functors into V .This enables them to recover different standard notions of automata by choosing V appropriately, and they further analyzed the determinization for Rel-automata using the Kleisli adjunction between Set and Rel.In this paper, we revisit Colcombet and Petris ¸an's analysis from a fibrational perspective, building on Melliès and Zeilberger's recent alternative but related definition of categorical automata as functors p : Q → C satisfying the finitary fiber and unique lifting of factorizations property.In doing so, we improve the understanding of determinization in three regards: Firstly, we carefully describe the universal property of determinization in terms of forward-backward simulations.Secondly, we generalize the determinization procedure for Rel automata using a local adjunction between Span(Set) and Rel, which provides us with a canonical forward simulation.Finally we also propose an alternative determinization based on the multiset relative adjunction which retains paths, and we leverage this to provide a canonical forward-backward simulation.
DOI: 10.4204/eptcs.429.11
Author: Thea Li
Institution: Université Paris Cité
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4414402225